This paper deals with a discrete predictive control design for motion control of robotic systems. The design considers time-varying state-space robot model. It is assumed that used robot state has to be estimated from measured robot outputs. These outputs represent controlled quantities including a bounded noise. Considering this arrangement, the paper introduces a novel solution to the state and noise parameter estimations based on linear programming that is incorporated in the control design. Estimated states are utilised for updating state-dependent elements in the robot model and for control design itself. Estimated noise parameters are employed in advanced tuning of control parameters, namely penalisation matrices. The proposed theoretical outcomes are demonstrated on one multi-input multi-output robot-manipulator as a specific representative of robotic systems.